Iso-entangled bases and joint measurements

TL;DR

This paper systematically classifies iso-entangled bases for joint measurements on two qubits, revealing unique properties of the Elegant Joint Measurement in quantum networks and discussing extensions to higher dimensions.

Contribution

It provides a complete classification of iso-entangled bases for two-qubit joint measurements and analyzes their role in quantum networks, especially with Werner states.

Findings

Elegant Joint Measurement yields permutation-invariant distributions with Werner states

Complete classification of iso-entangled bases for 2-qubit measurements

Partial results on higher-dimensional entangled measurements

Abstract

While entanglement between distant parties has been extensively studied, entangled measurements have received relatively little attention despite their significance in understanding non-locality and their central role in quantum computation and networks. We present a systematic study of entangled measurements, providing a complete classification of all equivalence classes of iso-entangled bases for projective joint measurements on 2 qubits. The application of this classification to the triangular network reveals that the Elegant Joint Measurement, along with white noise, is the only measurement resulting in output permutation invariant probability distributions when the nodes are connected by Werner states. The paper concludes with a discussion of partial results in higher dimensions.